Divisibility Rules

A Divisibility Rules is a shortcut method of discovering whether a given number is divisible by a certain divisor without performing the division, usually by examining its digits. Although there are divisibility rules for numbers in any base, and they are all different, this section presents rules.

Divisibility Rules of some numbers are given below:

A Number is divisible by:

If

Example

2

Its unit's digit is 0,2,4,6 or 8.

36 is divisible but not 39.

3

The sum of its digit is divisible by 3.

144 (1+ 4 + 4 = 9 ÷3 = 3) yes

4

The number formed by its digit in ten's and unit's place is divisble by 4.

348 (48 ÷ 4 =12) yes

5

Its unit's digit is 0 or 5.

450 , 855 is divisible but not 806.

6

It is divisible by both 2 and 3.

114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = which is not a whole number) No

7

If you double the last digit and subtract it from the rest of the number and the answer is:
1) 0, or
2) divisible by 7
(Note: you can apply this rule to that answer again if you want)